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Abstract
Surface deformation by coating stress is compensated by prefiguring the substrate with a radially nonuniform layer of dense silica. Stresses in the compensation layer and reflector are modeled using finite element analysis to determine the optimal thickness profile, with the deposited coating reducing the surface deformation by 90%. This process is intended to allow implementation of both the compensation layer and the traditional multilayer coating in a single vacuum cycle.
© 2019 Optical Society of America
1. INTRODUCTION
Ion-beam sputtering [1], magnetron sputtering [2], plasma-ion–assisted deposition [3], and ion-assisted deposition [4] are energetic deposition technologies that in general lead to compressively stressed thin films. While compressive stresses are preferred relative to tensile stresses, since tensile film stress can lead to cracking of the film on the substrate, film stresses of sufficient magnitude can lead to significant deformation of the substrate-surface flatness or necessitate much thicker substrates to limit bending [5]. This becomes problematic for larger-aperture substrates, particularly for thick coatings on relatively thin substrates.
The effects of coating stress have traditionally been mitigated by coating the back surface of the optic with a comparable film stress/thickness combination [6] or fabricating the optic surface with a curvature to counteract the net effect of the film stress [7], yielding a flat coated surface. More recently, an approach requiring not only rear-surface deposition but also photoresist application, complex patterning, etching, and precision cleaning has also been demonstrated [8]. In practice such efforts are costly and somewhat difficult to implement since such a stress-compensation layer would require an additional coating deposition, and prefiguring the optic surface leads to fabrication specifications that are often impractical. The lithographic approach to large-optic processing, similar to the production of large-scale diffraction gratings, increases optical-coating costs by at least an order of magnitude and is impractical for most large-scale production purposes. Stress reduction by process modification/refinement can lead to partially densified/porous films with relatively unstable mechanical and optical properties, making such an approach unattractive for precision applications.
The approach to minimizing optic-surface deformation pursued in this work is by depositing a film with a radial thickness gradient to correct the surface deformation of a compressive optical coating, essentially by prefiguring the substrate surface. By establishing an intentionally nonplanar surface profile, the resulting combination of a concave substrate surface and a compressively stressed plane-parallel coating can theoretically yield a resulting flat surface with a corresponding flat optical reflected wavefront. Calculation of forces and the resulting film/substrate deformation is performed using finite element analysis (FEA); for a given substrate and compressively stressed film, the intermediate compensation layer can be designed and optimized to yield a nominally flat surface. This technique was used to design a silica film-thickness profile with a physical thickness of the order of 6.7 µm at the periphery in order to compensate the stress of a 3.3-µm-thick multilayer coating on a 100-mm-diameter $ \times \;{3}$-mm-thick fused-silica substrate. This experiment was performed in two separate vacuum cycles, first with the deposition of the nonuniform layer through a shadow mask to yield the desired thickness profile, and then the multilayer deposition using the standard chamber configuration. Ideally, this process would be adapted to deposition in a single vacuum cycle, using a mechanical means to insert and remove the shadow mask as needed.
The surface deformation of the substrate was reduced by approximately 90% by using this compensation technique, with further refinement of the mask design and film thickness expected to lead to further improvement. Such an approach is advantageous to both the final system performance and the deposition process, given the potential to minimize coating-system time while improving the optical surface flatness.
2. BACKGROUND
Substrate deformation resulting from coating stress in a plane-parallel layer or series of layers is well described by Stoney’s equation [9]
where $\sigma $ is the stress in the film, $R$ is the radius of curvature of the surface, $E_{\rm s}$ is Young’s modulus of the substrate, $\nu_{\rm s}$ is Poisson’s ratio for the substrate, and $t_{\rm f}$ and $t_{\rm s}$ are the thickness of the film and substrate, respectively. Stoney’s equation is an approximation, suitable only when ${t_{\rm f}} \ll {t_{\rm s}}$, which determines the radius of curvature for the resulting substrate surface as a function of the in-plane stress of the coating. Compressive film stresses, such as those typically realized from energetic deposition processes, lead to a convex coated surface, while tensile film stress results in a concave coated surface. Although surface deformation can be minimized by increasing the substrate thickness or reducing the film thickness, wavefront errors resulting from coating stress are problematic for the overall performance of optical systems.Thin-film nonuniformity can be corrected by using shadow masks and substrate motion to yield highly uniform optical coatings [10,11]. The same principles can also be applied for the deposition of intentionally nonuniform coatings in order to achieve spatially varying properties such as graded and stepped filters. This masking approach can likewise be applied to form a layer of a specified thickness profile, provided that the substrate is centered on the axis of rotation, to yield a surface change/correction; such a deposition could be used to modify a spherical surface to an aspheric profile or to prefigure the surface to compensate for the anticipated film stress of a thick multilayer coating. This approach is illustrated in cross section in Fig. 1. The optic [Fig. 1(a)] is initially flat. A compressive silica coating is deposited [Fig. 1(b)], with the film thickness much greater at the edge of the optic than at the center, but the film also results in some deflection of the substrate. The substrate is bent in a convex manner, but the resulting surface (coating + substrate) is now concave as a result of the film-thickness profile. The deposition of a uniform-thickness coating on the combined substrate/corrective layer [Fig. 1(c)] yields a flat surface once again, even though the substrate is deflected further in the same direction by the compressive film stress.
Fig. 1. The approach for stress compensation is shown in cross section, with (a) the initial flat substrate; (b) the deposition of the compressive, graded layer deflects the substrate convex, while the coating surface is now concave; and (c) the combined substrate/graded layer/uniform-thickness multilayer results in a distorted substrate, but the coating surface (and therefore reflected wavefront) is nominally flat.
The film-thickness profile of the compensation layer must be carefully established to correct not only the surface deflection from the multilayer but also for the surface deflection from the compensation layer itself. Therefore, this approach to stress compensation will be valid only for combinations of compensation-layer stress and substrate thickness for which the coated surface becomes more concave as the thickness of the compensation layer is increased. Thicker substrates will require less of a compensation layer, and thinner substrates will require a greater compensation layer. Since this layer has a variable thickness profile, it cannot be modeled with Stoney’s equation and must be evaluated using FEA.
Fig. 2. Compensation layer film-thickness profile, based on the use of a compressively stressed silica layer to correct the surface flatness for a compressive mirror coating. As shown, the film is thicker at the periphery than either the multilayer reflector or the sag of the coated surface since the layer must overcome the surface distortion resulting from both the multilayer reflector and the silica compensation layer.
Fig. 3. (a) 1.4-m coating chamber with electron-beam evaporation, plasma-ion–assisted deposition, and planetary substrate rotation. (b) The uniformity mask is centered on the 100-mm planet, such that the vapor flux is masked throughout the deposition.
3. EXPERIMENT AND RESULTS
The deflection of the substrate surface as a result of depositing a 38-layer, 3.3-µm-thick niobia/silica high-reflector coating (with two hafnia layers and one alumina layer) using plasma-ion−assisted deposition (PIAD) as described previously [10] results in a calculated (compressive) stress of $ - {135}\;{\rm MPa}$. This stress was modeled on a 100-mm-diameter $ \times \;{3}$-mm-thick fused-silica substrate using Ansys FEA software, and a silica compensation layer was incorporated. The initial compensating layer design was based on the expected deviation from the multilayer, as if the compensation layer, with near-zero thickness at the optic center, contributed no additional stress-induced deformation to the substrate (only a physical thickness growth on the surface). Of course, there is a stress-induced deformation resulting from the silica compensation layer, but this deformation is not spherical and does not follow Stoney’s equation since the layer thickness is not uniform. Once this layer is incorporated into the FEA model, the overall surface flatness can again be calculated, and it is apparent that while the silica film-thickness profile corrects the previous surface deformation, the silica stress adds an additional (nominally) convex curvature of reduced magnitude to the coated surface. This deformation must also be corrected in order to achieve a flat surface profile, with additional compressively stressed silica simultaneously improving the flatness and deflecting the surface in a convex manner. The required layer profile to achieve an optimal surface flatness, compensating for both the multilayer and compensation-layer deflections, was refined in the FEA model, providing a targeted radial-thickness profile for the silica layer to yield a nominally flat coated surface. The film-thickness profile of the compensation layer is shown in Fig. 2.
Fig. 4. Change in the surface figure of a 100-mm-diameter, 3-mm-thick fused-silica substrate as a result of coating with an all-dielectric mirror coating with or without a silica stress-compensation layer (as-fabricated surface flatness subtracted from all subsequent measurements). (a) Control (mirror coating only) surface figure, at 5.4 waves of deviation from flat ($\lambda = {633}\;{\rm nm}$). (b) After coating with the silica compensation layer, the surface is 3.5 waves concave. (c) Once the high-reflector coating is deposited, the combination of the two coatings results in a nominally flat optic, with the change in surface flatness $\sim{10}\% $ of that resulting from the high-reflector coating alone. A slightly thicker compensation layer could further improve the surface flatness. ${p} - {v}$, peak to valley.
The silica compensation layer was deposited through a mask mounted approximately 2.7 mm beneath the planet, centered on the optic undergoing planetary rotation as shown in Fig. 3. The mask remains centered on the rotating substrate throughout the deposition; as a result, the mask design is simply a normalized percentage of open space, based on the desired profile. For example, a thickness at the perimeter of the 50-mm-diameter optic of 9.5 µm, 5 µm at a radius of 38.3 mm, and 0 at the optic center corresponds to an open space of 360°, 189.5°, and 0°, respectively. This can be understood as the overall thickness of 9.5 µm will be deposited without any mask obscuration, 52.63% of the total thickness (5 µm) will be achieved by that portion of the circle remaining open (52.63% of 360° is 189.5°), and no thickness will be deposited if the mask fully obscures that region of the substrate (0° of open space).
Practical fabrication requires that the entire perimeter should not be open, so the mask angles can be scaled by a constant (0.9) while scaling the coating deposition by the inverse of the same constant (1.11). The overall deposition thickness for an unmasked sample can then be scaled by 1.11 to compensate for the magnitude of the shadow for the thickest film in the masked compensation layer at the periphery of the optic.
The substrate was measured for surface flatness on a 4-in. Zygo Verifire 633-nm interferometer before coating, after deposition of the compensation layer, and then again after deposition of the mirror coating. For the purposes of this qualification test, the uniformly deposited reflective coating (no mask) was centered at 633 nm to minimize the impact of coating phase-on-reflection on the interferometric measurement. Once the process is qualified, with a well-understood impact on surface flatness, any coating could be deposited with minimal impact on the flatness measurement (assuming a relatively uniform multilayer deposition, with a corresponding flat phase front). The uncoated optics all had a nominal deviation from flat of 0.3 waves of power, or approximately 0.2 µm. The uncoated measurement of each substrate was subtracted from the compensation and overall measurements to isolate the effects of this experiment. In addition, a control sample was included in the high-reflector deposition to measure the deformation without the compensating layer. The results are shown in Fig. 4.
It is apparent in Fig. 4(c) that the peak-to-valley deviation of the optic with the corrective layer is almost 90% less than that of the control surface flatness in Fig. 4(a) (0.57 versus 5.43 waves at 633 nm). There is also a small circular error near the optic center visible in Fig. 4(c), indicative of a rapid change from no coating at the optic center to a nonzero thickness; this transition should ideally be smoothed somewhat by improved mask design or spacing optimization from the optic surface. Furthermore, it is apparent that increasing the deposited thickness of the corrective layer slightly would have further improved the surface flatness since Fig. 4(c) is clearly dominated by a spherical-like term with the edge being low and the center the highest point (the compensation that the corrective layer is intended to provide). Since the mask irregularly shadows the deposition, further calibration is needed to refine the layer thickness; regardless, this approach has been shown to substantially reduce the deformation of an intentionally thin optic while depositing on only a single optical surface.
4. CONCLUSIONS
The stress-induced wavefront deformation of a substrate by a compressively stressed, dense optical coating can be compensated by depositing a nonuniform silica layer through a shadow mask. The thickness profile must be carefully considered to account for both the deformation from the primary multilayer coating as well as any stress-induced deformation from the compensating layer itself. The deposition of a controlled silica layer profile with a nominal thickness of 7.5 µm was used to correct the deformation from a 3.3-µm-thick high-reflector coating. The deflection of a 100-mm-diameter $ \times \;{3}$-mm-thick fused-silica substrate was reduced by $\sim{90}\% $ by deposition of a silica compensation layer.
This approach can be readily implemented in the manufacture of precision optical coatings by ion-beam or magnetron sputtering, requiring only the mechanical movement of the mask into position during application of the compensation layer. This method is ideal for reflective coatings on precision substrates in regular production processes; the efforts required to compensate for deflection of single substrates may make such an approach impractical without additional justification as to the selection of this technique. Such an approach minimizes the need for post-processing, such as annealing, or additional coating depositions to address stress-induced wavefront deformation. Any long-term stress instabilities can also be incorporated in the compensation-layer design, assuming sufficient quantitative characterization of the film-stress evolution as a function of time.
Future work utilizing this approach is anticipated to refine the flatness-compensation technique, particularly for thicker substrates for precision applications; the substrates used in this proof of concept were intentionally thinner to make the problem worse and the impact of the improvement more readily apparent. In addition, this approach can be utilized as a means of altering the surface figure of a substrate, in an “additive-deposition” approach, in order to modify a nominally flat or spherical surface figure to a slight curvature or an aspheric profile. Manipulation of a spherical figure to that of an aspheric may provide a means of rapid, cost-effective precision-surface-figure generation.
Funding
National Nuclear Security Administration (DE-NA0003856).
Acknowledgment
This report was prepared as an account of work sponsored by an agency of the U.S. Government. Neither the U.S. Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the U.S. Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the U.S. Government or any agency thereof.
Disclosures
J. B. O.: Vacuum Innovations LLC (I, E); J. E. S. : none; B. M. C.: none.
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